Finite Group Databasebeta

← #21461336

Subgroups — #21461336

Order 7808.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840767C211yesmaximal, characteristic
2D61⋊(C4⋊C8)C211yesmaximal, characteristic
3#16840622C212yesmaximal, complemented
4#16840621C212yesmaximal, complemented
5#16840316C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×D61⋊C8—21no—
8#14519844—21no—
9#14519844C2212yes—
10#14519844C2212yes—
11C4⋊#92420—21no—
12#14519776C2211yescharacteristic
13#14519775C2211yescharacteristic
14#14519767—21no—
15#14519757C411yescharacteristic
16#14519755—21no—
17#14519753C411yescharacteristic
18C4×Dic122—21no—
19C4×Dic122C411yescharacteristic
20#14519734—21no—
21C42×D61C2211yescharacteristic
22C4×Q8×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×C4×D61C2×C411yescharacteristic
25C2×C4×D61D411yescharacteristic
26C2×C4×D61D411yescharacteristic
27C2×Dic122—21no—
28C2×Dic122C2×C411yescharacteristic
29C2×#92420—22no—
30C2×#92420—22no—
31#11758213—42no—
32D61⋊C8—42no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C411yescharacteristic
35C42×C61—21no—
36C42×C61C2×C411yescharacteristic
37#11758198—21no—
38#11758198—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C411yescharacteristic
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C22×D61C22⋊C411yescharacteristic
51Q8×C61—41no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61C22⋊C411yescharacteristic
60C2×Dic61C2×D411yescharacteristic
61C2×Dic61C2×D411yescharacteristic
62C4×D61—21no—
63C4×D61—21no—
64C4×D61—41no—
65C4×D61SD1612yes—
66C4×D61Q1612yes—
67Dic122—41no—
68Dic122—41no—
69Dic122—41no—
70#92420—42no—
71#92420—42no—
72C22×C61C2×C22⋊C411yescharacteristic
73C2×D61—21no—
74C2×D61—21no—
75C2×D61#10312yes—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—41no—
79C4×C61—41no—
80C4×C61#10312yes—
81Dic61—21no—
82Dic61—41no—
83Dic61—41no—
84Dic61C2×SD1611yescharacteristic
85Dic61C2×Q1611yescharacteristic
86Dic61AGL(1,ℤ/8)11yescharacteristic
87Dic61#13711yescharacteristic
88#1550—611nomaximal, Sylow
89C2×C61#41311yescharacteristic
90C2×C61C2×#10311yescharacteristic
91C2×C61#41711yescharacteristic
92D61—22no—
93#533—611no—
94#423—611no—
95C2×C4⋊C8—611no—
96#333—612no—
97#332—612no—
98C61#155011yescharacteristic, complemented, Sylow
99C2×M16—1221no—
100C22×C8—1221no—
101C4⋊Q8—611no—
102C4⋊Q8—611no—
103#125—1221no—
104C22⋊Q8—611no—
105C22⋊Q8—611no—
106C22⋊Q8—1221no—
107C4×Q8—611no—
108C4×Q8—1221no—
109C4×Q8#692311yescharacteristic
110#117—1221no—
111C2×C42—611no—
112C4⋊C8—612no—
113C4⋊C8—612no—
114C4⋊C8—1221no—
115C4⋊C8—1221no—
116C2×Q8—611no—
117C2×Q8—1221no—
118C2×Q8C2×#692311yescharacteristic
119C22×C4—611no—
120C22×C4—611no—
121C22×C4—611no—
122M16—2442no—
123C2×C8—1222no—
124C2×C8—1222no—
125C2×C8—2442no—
126C4⋊C4—21no—
127C4⋊C4—611no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4C2×#692311yescharacteristic
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C42—21no—
138C42—611no—
139C42—611no—
140C42—611no—
141C42—1221no—
142C42C2×#692311yescharacteristic
143C23—611no—
144Q8—41no—
145Q8—2441no—
146Q8—2441no—
147Q8—2441no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—612no—
153C2×C4—612no—
154C2×C4—611no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—2441no—
160C2×C4C22⋊#692311yescharacteristic
161C2×C4C22⋊#692311yescharacteristic
162C2×C4C22×#692311yescharacteristic
163C8—2442no—
164C8—2442no—
165C22—612no—
166C22—1221no—
167C22—1221no—
168C22C2×C22⋊#692311yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—611no—
174C4—611no—
175C4—611no—
176C4—611no—
177C4—1221no—
178C4—2441no—
179C4—2441no—
180C4#1451984012yes—
181C2—1222no—
182C2#1684074811yescharacteristic
183C2C2×#1451984011yescharacteristic
184C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1550
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #16840622C2semidirect
4. #16840621C2semidirect
98. C61#1550semidirect